Posted
by
timothy
on Thursday April 22, 2010 @06:09PM
from the all-those-in-favor-and-then-some dept.

An anonymous reader writes "In Truro, Massachusetts (a town on Cape Cod), a zoning decision came up for vote, where the results were 136 for, 70 against. The vote required 2/3 approval to pass. The Town Clerk and Town Accountant believe that since .66 * 206 is less than 136, the vote passes. However, an 'anonymous caller' noted that a more accurate value of 2/3 would require 137 (or perhaps even 138 votes) for the measure to be considered passed. The MA Secretary of State and State Attorney General are hard at work to resolve this issue."Updated 20100422 23:55 by timothy: Oops! This story is a year old (rounding up), which I didn't spot quickly enough. Hope they've got it all worked out in the meantime.

It should at least be rounded, if not just simply rounded up (i.e., ceiling). It's talking about people; you can't have 3.5 people, so if you want "more than 3" people then you need to go up to 4 people.

No, they definitely didn't round up, they truncated a number that was never accurate to begin with. 206*2/3 takes a half second longer to punch in than 206*0.66, if that. Why were they ever using 0.66 to begin with?

They would need 138 votes. 137 is less than 2/3rds. 0.66 != 2/3. Plain and simple.

But I think it's amusing to say the least -- splitting hairs on a vote.

Really, the who notion of voting is severely flawed from a mathematical point of view. One extra vote makes all the difference between whether or not a bill is implemented. What is the intrinsic importance of making it 2/3rds? Why not 3/4ths? 1/2? 5/8ths? What is the significance of 2/3? Seems arbitrary.

But then, that is the difference between law and mathematics, I suppose. 20 years and 364 days old, you're too young to drink, it's illegal, and there are sanctions. 20 years and 365 days -- 21 years old, and it's perfectly legal. But what is the significant difference in a person at 20 years 364 days vs. 20 years 365 days? Is there some sort of "maturity switch" that is magically flipped? Do the gods of time descend upon you and bestow you with something special?

We humans make so much ado over meaningless arbitrary demarcations. Life situations are fuzzy and spread out, not the digital of "on/off". It all seems rather a bit silly! Splitting arbitrary hairs without real meaning.

Under my proposed law, during the years between 16 and 21 noninclusive, the probability of being chargeable, upon discovery, with underage drinking shall be determined by interpolation through a truncated logistic function. n'hey.

While drawing these arbitrary lines is silly, it is often far sillier to not draw them in the universe we live in.

Making silly arbitrary decisions is a necessary part of life. Life situations aren't that fuzzy except at the quantum level. Even little things like which hand to use, whether to breath in or out. And even if the Many Worlds Interpretation is correct, it's not that fuzzy in each path of the universe.

Say a car is about to hit you, you could jump either left or right to save yourself. The neurons in your brain are going to have to make a decision. Say you jump right, you think all the neurons participating in the decision wanted to go right? I doubt it, some would have wanted to go left. But you cannot satisfy all of them. You can't go both left and right, unless you wait for the car to split you in two.

Back to your question, there is no magical maturity switch. Some people never even become mature. So what? With our current technology we are not able to practically put you 60% in jail and 40% out of jail at the same time, just because you are actually "60% mature".

And it's costly to put in all the shades of gray for the different percentages of "maturity". Some countries do cater for a few categories: juvenile prisons, probation, etc.

So there are very many arbitrary lines in laws: when it's legal to abort a fetus/baby, when does a child become an adult.

There's definitely much silliness that should perhaps be fixed. For example, in many countries you might be legally considered old enough to sign up as a soldier, but not do other "adult things". This to me is silly. If you are going to be old enough to kill others and risk your own life, you should be considered old enough to do the other adult stuff. Otherwise, you shouldn't be considered old enough to be a soldier (unless the country is in such a bad/desperate state that you might as be allowed to be a soldier).

There are even better reasons to draw sharp, arbitrary lines - to make the outcome of the law predictable. If the line between between old-enough-to-drink and not-old-enough-to-drink was fuzzy, or the court was required to decide if you were mature enough to drink, it would be almost impossible for the individual to determine when it was safe to drink.

It's trivial to multiply 206 by 2/3 on a calculater, and it in no way involves any decimal figure until the result is shown.

206 * 2 = 412. 412/3 = 137.3~, or 137r1 via long division.

It's pretty clear, the law requires a 2/3 majority, and 137 is not even a 2/3 majority, let alone 136. This is maybe third or fourth grade level math here people, and it's kinda sad that there is even any confusion about it..66 is not 2/3, it's a little less than 2/3 and it does not count if the law says 2/3.

This is maybe third or fourth grade level math here people, and it's kinda sad that there is even any confusion about it..66 is not 2/3, it's a little less than 2/3 and it does not count if the law says 2/3.

You know good and well these assholes were the kids who used to ask "Why will I ever need to know this stuff in real life?" when they were kids.

I don't know much about python, but if you're using Integer data types, you're taking the wrong approach. I assume Python implicitly converts 206 to an integer, and that division of integers results in integers. 206.0 would be currency if not an actual float, then, making the results floats.

But the best way to calculate fractional multiplication is get all of your multiplications done first, then do a single division. The last thing you want is a rounding error, so you do it last and it's the last thing

I don't know much about python, but if you're using Integer data types, you're taking the wrong approach... 206 * 2 / 3

This story would be much more interesting if they did use integer division as 2 / 3 * 206. In fact since the law didn't declare the type for number_of_votes, I suggest we fall back to fortran conventions.

Actually, thats not even correct. Its a repeating number, but, its wrong to round in the middle of an operation. You always round the final value, not the intermediary value. You take 2/3 and then round, not round and then multiply.

You would think any dumbass would know how to multiply fractions on a calculator - it doesn't take any fancy functions, just a very very basic understanding of what a fraction is.

When it says 2/3, you use 2/3, not a decimal of anything. (206*2)/3, that's it. Done. The answer is 137.3~, and it's as accurate as is humanly possible. The only number of voters that satisfies the 2/3 majority requirement is 138.

This is so incredibly simple that I can't believe I'm reading scores of responses about significant digits and rounding, etc. For a motion to be passed by a 2/3 majority, at least twice as many people have to vote in favour as those who vote against. Since 136 is less than 70*2, the vote fails. No calculator required, no consideration of significant digits. It's the kind of thing a reflective schoolchild should be able to reason out, frankly.

Interestingly, the U.S. Constitution was written with this passage about the census:

Representatives and direct Taxes shall be apportioned among the several States which may be included within this Union, according to their respective Numbers, which shall be determined by adding to the whole Number of free Persons, including those bound to Service for a Term of Years, and excluding Indians not taxed, three fifths of all other Persons.

So each non-free person (slave) counted as 3/5 of a person... That's Art

i was taking this basic 'intro to' math class. i got the first exam back, and most of my answers were marked incorrect when i knew they were right. the supposedly correct answers were written on my test and some were relatively close, while some were not. perhaps you can guess where this is going.

i asked the teacher what was up and as she was checking my test, i saw her answer sheet had her work shown on it and realized quickly what the problem was. yes, she had rounded all the fractions to two place dec

One guy made a stupid mistake. It doesn't mean someone can't do math, it just means he got one math question wrong--the failure wasn't so much the bad math, it was (1) the failure of him to check his math a second time when the vote came out as close as it did, and (2) the fact that they didn't have someone else check it.

It's okay to not notice an extra decimal place on a first approximation. It's not okay if it suddenly might matter because you're within a vote of n

I'd side with the commenter that more than 136 votes are needed. Now, whether or not you truncate the decimal or round it, I'm not sure. In this case it doesn't matter though, it comes to 137 either way.

Now, whether or not you truncate the decimal or round it, I'm not sure. In this case it doesn't matter though, it comes to 137 either way.

Nope, it doesn't. The correct answer is 138 votes to pass. As you noted, 206 times 2/3 is 137 plus one third. 137 votes is less than two thirds of 206; it therefore doesn't pass either.

(If the supermajority calculation is confusing, consider a conceptually-easier simple majority (1/2) case. In the hypothetical case of 101 voters, a pass is 51 votes - being the first integer greater than 50.5 - not 50.)

136/206 = 0.66019
137/206 = 0.66505
138/206 = 0.66990
2/3 = 0.66667
Clearly the measure does not pass with 2/3 of the vote. Even if you round off to 2 digits you would get 136/206 = 0.66, and 2/3 = 0.67, so it still doesn't pass.

The ratio of 2/3 to 1/3 is 2:1. In order for a measure to pass by a two-thirds vote, the majority must have more than twice as many as the minority. 136 is less than two times 70, so the vote does not pass.

Actually having twice as much is sufficient. They don't need more than twice. If it had been 140 to 70, it passes. And failing this kind of math, simple election and voting math, should be sufficient to remove both individuals from their jobs.

No. A majority vote requires 50% + epsilon to pass. However, a 2/3 vote typically requires that the majority must have at least twice as many as the minority, not "more than twice as many". Which is to say, if there are three people voting, only two voting yea passes the bill, not three.

Voters did approve one of four petitioned zoning articles, one that would require cottage colonies to be in operation for at least three years before they can be turned into condominium ownership. Zoning articles require a two-thirds majority and the first vote was close, counted as 139 in favor and 64 opposed. A recount was held that was tallied at 136-70 and declared to be passed by Town Clerk Cynthia Slade, utilizing a multiplier of 0.66 to determine two-thirds, the figure the town has always used. Unfortunately, this vote was so close that the inaccurate fraction made the difference, and several months later the attorney general’s office negated the approval as not meeting the two-thirds threshold.

Yup. The Massachusetts Attorney General reviews all Town Meeting articles, and usually takes a few months to certify the results as valid and legal. This one would have been pretty obvious, but there were a bunch of other articles to review from the same meeting, and there are several hundred towns, so the number of articles pending review could easily be several thousand.

"one zoning amendment which the voters passed in April - to require cottage colonies to operate as such for three years before conversion to condos is permitted - was reversed on a vote count challenge by a recent decision of the Mass. Attorney General's office. "

Updated 20100422 23:55 by timothy: Oops! This story is a year old (rounding up), which I didn't spot quickly enough. Hope they've got it all worked out in the meantime.

Generating news isn't simple. You have to investigate, contact the sources, write the article, correct it, publish it in a readable way, etc, etc.

Agregating news isn't that hard. All you have to do is check the source, the date and place of the article, if it's serious and still relevant, write a small summary (or cut and past it from the article) and submit. Not that hard at all. Google news does a better job than Slashdot at it. A damn perl script does a better job than 20+ slashdot editors. Even Fark is doing better than slashdot. If you post some old copypasta on the randomness and caos that is/b/, it'll be spotted instantly. The 13 year old kids at/b/ do a better job than slashdot's team of editors.

I usually don't complain about article quality, dups, etc. I believe it's better to just let it go and move on. I say "hey, anyone can make a mistake". But it just gets worse everyday. We trust slashdot. We just spent a lot of our time discussing this issue, and trying to provide meaningful answers. It turned out to be an issue that happened almost a year ago. That is worse than reading slashdot on April 1st (at least you KNOW it's all bullshit on April fools day).

Even taking all the stupid trolls into account, this community is much more valuable than the site that is hosting it. Yes, we can be a bunch of assholes sometimes, but I believe this is still true: Slashdot's community is la creme de la creme of the Internet. Just tell me of any other place where you can get a high profile open source developer, a NASA researcher that has written code for the Shuttle, a guy from Star Trek, a lawyer that understands copyright law, one of the founders of Apple, the Father of quake, an employee from almost every single technology corporation in the world, plus a huge crowd of engineers, coders, technology enthusiasts, writers, philosophers, sysadmins, doctors, lawyers, politicians, and generally smart people. The Slashdot community is amazing. Unique. I can't think of any other place with such diversity and such a high concentration of people that matters. Don't get me wrong, I'm not saying that/. readers are some kind of superior race. I'm just saying that the distribution of people in/. isn't average. We certainly have less cab drivers and more world changers than any other community out there. What worries me, is that the the site hosting that community is not up to the task. I love Slashdot. I've been in here for a long long time, and I have no intention of leaving. This is an off topic comment, and it'll certainly be flagged as such... But I just felt like sharing this lines with you. What can we do to improve this place? it is, after all, like a second home to many of us.

The analogy fails, though, as there's no error of measurement here. The area of a circle with a radius of "the integer 25" is 625*pi exactly, not some decimal measuement. 2/3s of 206 is 137+1/3 exactly, not some decimal measurement.

How do you determine the area of a circle with a radius of 25.0 units, without "expressing an infinitely repeating number as a finite value"?

Pi is not a repeating number, it's an irrational number. When you're dealing with an irrational number the only way you can express it is by itself. Pi is pi, that's it. The only value equal to pi is pi. If you're using pi in a calculation, you don't use a fraction, you use pi. 22/7 is sometimes used to estimate pi, but that's not correct either.

Thankfully, legislative decisions are not based on irrational numbers, they are based on fractions.

137 is less than 137 1/3, so 137 is not a 2/3 majority.138 is greater than 137 1/3, so 138 is a 2/3 majority.

Done. You can keep the 138 figure on hand to remind yourself, but it isn't necessary, just do 206 * 2/3 to get the minimum number of votes needed. It isn't hard.

This story and some of the posts have really been pretty sad, half the people on slashdot are perpetuating the same error the clerk made, they are simply doing it more accurately. The other half have come up with convoluted ways to check whether a number meets the criteria.

Significant figures are important. In this case, the 2/3rds rule, being a constant, MUST be taken to at least 3 digits. Otherwise why not just use 0.6 instead of 0.667

Significant figures has absolutely nothing to do with it. They are for making measurements in a non-discrete space. All that's going on here is counting--there's no error, so no need for significant figures. Why on earth would you approximate a constant anyways? In any event, your rule for 'at least 3 digits' is completely arbitrary and useless. With enough votes, one could show that taking 'at least 3 digits' would still yield an incorrect result.

Since the original post is so brief, it's difficult to determine its intent. However, the usual intimation of such quotes is to imply that the 3/5ths valuation was immoral because slaves should have been counted fully, i.e., as 5/5ths.

But this is exactly counter to the various political goals of the time: the northern colonies, who were more generally against slavery (yes, there was still slavery in the North, but I'm describing averages) wanted the slaves to not be counted at all, while the southern colon